The purpose of President Obama’s visit to Israel finally emerged on Thursday, in the ebullient afterglow of the speech that was billed as the centerpiece of his trip, and lived up to the billing. After a first term spent trying to alter the mechanics of the negotiations between Israelis and Palestinians over the land they both claim — tinkering with settlement freezes, summoning leaders to the White House — Obama decided on a new approach to Middle East peace: he’d talk them into it.

“He’s so good, I loved it even though I don’t agree with some of what he said,” says Gila Kordana, descending a staircase from the balcony in a crowd buzzing with the experience. Such as? “I’m not really for the idea of two states,” she says, not a small thing. Nor was she much taken with Obama’s take on the young Palestinians he’d seen earlier the same afternoon at the West Bank city of Al Bireh. “Talking to them,” he said, “they weren’t that different from my daughters. They weren’t that different from your daughters or sons.”

“My brother’s in the IDF [Israel Defense Forces], and they deal with 9-year-old kids who throw bottles,” Kordana says. “So I didn’t go for that part about them being just like us. ‘My daughters, your daughters, their daughters,’” Kordana says, paraphrasing Obama’s plea for “empathy” and seeing your own in the faces of the other: “You can’t put them in the same triangle.”

The reality lurking outside the afterglow was not lost on the White House. Obama understands that the two-state framework is in danger of collapse — the idea that the competition between Jews and Palestinians can be resolved by negotiating a sovereign Palestine on the West Bank, which Israel has occupied since 1967, and Gaza Strip, which remains virtually sealed off by the IDF. But the new government assembled by Israeli Prime Minister Benjamin Netanyahu is officially committed to resuming the talks, and Obama spent hours with both Netanyahu and Palestinian Authority President Mahmoud Abbas trying to bridge the mistrust between the two.

He’s made progress, according to a senior Obama Administration official. The larger problem is that their constituents have no faith in the talks anymore, either, especially the young people Obama is trying to coax. “They do not trust the two-state solution and vision anymore, and this is very dangerous,” Abbas said in a joint news conference with Obama in Ramallah, the West Bank city. “The younger generation no longer believes.”

Much the same is true in Israel, where polls for years have found a tension between the appetite for peace — still strong, in general — and an overwhelming pessimism that it will come to pass. The skepticism has devastated support for the “peace camp” in Israeli politics and empowered right-wing activists who support expansion of the about 200 settlements that amount to a slow takeover of the West Bank. Such activists hold senior posts in Netanyahu’s new government.

“It’s hard for political leaders to get too far ahead of your constituents,” Obama acknowledged in Ramallah. “But if we can get direct negotiations started again, I believe the shape of a potential deal is there.”

Therein lies the rationale for Obama’s three-day charm offensive in Israel, a full-court press designed to win over a Jewish population long wary of his attention to the Islamic world. The remedial effort appears to be going very, very well — with hard-shell Israelis marveling at the speed with which the nation has run into Obama’s arms. On 88 FM, a DJ spun Salt-n-Pepa’s “Whatta Man” and name-checked the President. On the front page of the Jerusalem Post, Herb Keinon wrote: “He had us at the word ‘shalom.’’’

The question is whether the newfound popularity will produce some newfound power of persuasion, especially on a topic as fraught as peace. His audience in Jerusalem was invitation-only and skewed young, Obama’s sweet spot: most were from universities inside Israel. “The reason he gave this speech to this audience today is because he believes people need to get invested in this,” a senior Obama Administration official said afterward. Mention of peace talks brought, like the lyrics of a nearly forgotten song, the vocabulary of diplomacy stretching back two decades now, which of course is much of the problem: it’s gone on too long and drifted into a world of its own. “If people don’t get reinvested in the idea that peace is in their interest and is possible, it doesn’t matter what kind of confidence-building measures you have,” the official said.

Can it work? In the convention center, the reception was enthusiastic, and not only for the portions that both stroked and stoked the Israelis — the eloquent enunciation of the inspiration African-Americans had taken from the Passover narrative, for instance, and the defiant proclamation: “Israel isn’t going anywhere.” The words brought a thunderous ovation — the kind Netanyahu receives, projecting the jut-jawed steadfastness that accounts for much of his popularity. But it meant more “when someone from outside said it aloud: ‘This is going to be a Jewish country,’” Kordana says. “It makes you feel more confident, more secure in your place.”

But there was also considerable applause heard for the challenging sections: Obama’s earnest case for believing again in a peace effort. At times the response was loud enough a stranger might have believed that the left wing in Israel is no longer referred to as Lonesome Doves.

“And now I’m not,” says Liat Biron, a graduate student in public policy at Tel Aviv University, one of the last leftist holdouts, as she left the auditorium, “because the President of the most powerful nation in the world feels the same way. “

But was anyone persuaded? “He made a very good argument,” says Dvir Goldstein, a student at Open University, looking past the enchantment of the “once-in-a-lifetime opportunity” to hear Obama speak. “I’ll certainly give new thought to the points that he offered.” He was already talking about it, after all.

Karl Vick has been TIME's Jerusalem bureau chief since 2010, covering Israel,the Palestine territories and nearby sovereignties. He worked 16 years at the Washington Post in Nairobi, Istanbul, Baghdad, Los Angeles and Rockville, MD.